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Chapter 2: Problem 4

Rewrite each expression using exponents. $$(0.8)(0.8)(0.8)$$

Short Answer

Expert verified
The given expression \((0.8)(0.8)(0.8)\) can be rewritten using exponents as \(0.8^3\).

Step by step solution

01

Identify the base and the number of times it is multiplied

In our expression, we can see that the number \(0.8\) is multiplied by itself three times: \((0.8)(0.8)(0.8)\).
02

Rewrite the expression using exponent notation

Exponent notation uses the base raised to the power of the exponent. In our case, the base is \(0.8\) and the exponent is \(3\) because it appears three times in the multiplication. We rewrite the expression as: \(0.8^3\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Base in Exponents
When dealing with exponents, understanding the concept of the 'base' is crucial. The base is the number that is being multiplied by itself.
In the exercise we are solving, the base is the number 0.8.
Think of the base as the foundation of your multiplication expression. It is the consistent number being repeatedly used in the multiplication process.
  • For example, in 0.8 x 0.8 x 0.8, the base is 0.8.
  • The base doesn't change; it's always the same number across the multiplication.
When you see a multiplication situation with the same numbers multiplying, always identify your base first. It simplifies the step of rewriting the expression using exponents.
Exponent Notation
Exponent notation is a shorthand way to represent repeated multiplication of the same number.
Instead of writing out lengthy multiplication expressions, you use an exponent to show how many times the base is multiplied by itself. For instance, instead of writing 0.8 x 0.8 x 0.8, you can write it using exponent notation as \(0.8^3\).
Here's how exponent notation works:
  • The number that is repeatedly multiplied is the base, in this case, 0.8.
  • The small number, written as a superscript, is the exponent. In this example, the exponent is 3, showing that the base 0.8 is used three times.
The exponent notation not only makes expressions easier to read but also provides a clearer understanding of the structure of the multiplication in operation.Remember, the exponent tells you how many times to multiply the base by itself!
Multiplication of Numbers
Multiplication is one of the basic arithmetic operations. It's essentially repeated addition. For example, multiplying 3 x 4 is the same as adding 3, four times: 3 + 3 + 3 + 3.
In the context of exponents, multiplication of numbers is simplified using the concept of the base and exponent. Instead of writing the whole multiplication sequence, we use an exponent to express the operation, such as rewriting multiple 0.8 multiplications as \(0.8^3\).
Some key points to understand about multiplication of numbers include:
  • When multiplying the same number, exponents help make this process faster and easier. Instead of manually multiplying every time, use the exponent notation!
  • Knowing the multiplication rules will make deriving expressions like \(0.8^3\) much quicker. It is especially useful when dealing with larger calculations or more complex problems.
Embrace exponents within multiplication as your tool to handle and simplify expressions efficiently.

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Most popular questions from this chapter

Simplify the expression using the product rule. Leave your answer in exponential form. $$\left(-7 t^{6}\right)\left(t^{3}\right)\left(-4 t^{7}\right)$$

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Write each number in scientific notation. -0.00000022

Perform the operation as indicated. Write the final answer without an exponent. \(\left(9.75 \times 10^{4}\right)+\left(6.25 \times 10^{4}\right)\)
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